Question

use the frequency distribution to complete parts (a) through (e).

a) determine the total number of observations.
b) determine the width of each class.
c) determine the midpoint of the second class.
d) determine the modal class (or classes).
e) determine the class limits of the next class if an additional class were to be added.

\

$$\begin{array}{cc} \\text{class} & \\text{frequency} \\\\ 7-14 & 9 \\\\ 15-22 & 5 \\\\ 23-30 & 0 \\\\ 31-38 & 0 \\\\ 39-46 & 2 \\\\ 47-54 & 1 \\end{array}$$

a) the total number of observations is

Explanation:

Sum the frequencies

Using the Frequency Distribution knowledge point

$$ N = 9 + 5 + 0 + 0 + 2 + 1 = 17 $$

Calculate class width

Using the Frequency Distribution knowledge point

$$ W = 15 - 7 = 8 $$

Find second class midpoint

Using the Frequency Distribution knowledge point

$$ M_2 = \frac{15 + 22}{2} = 18.5 $$

Identify highest frequency class

Using the Frequency Distribution knowledge point

$$ \text{Modal Class} = 7 - 14 $$

Determine next class limits

Using the Frequency Distribution knowledge point

$$
LATEXBLOCK0
$$

Answer:

a) The total number of observations is 17.

b) The width of each class is 8.

c) The midpoint of the second class is 18.5.

d) The modal class is 7–14.

e) The class limits of the next class are 55–62.